CHSH - the facts!

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

CHSH - the facts!

Postby Gordon Watson » Fri Jun 03, 2016 4:05 pm

*
An open plea to Joy Christian and Fred (and maybe others) to get the facts straight re CHSH - http://users.unimi.it/aqm/wp-content/uploads/CHSH.pdf. For your current position re CHSH (see your posts hereunder), weakens any other claim that you make in the contested area of local-realism.

NB: I am a determined local-realist so, in some places below, where the definition of "local-realism" needs to be clarified, I will add a "[sic]". But, please note, the CHSH inequality is unaffected by such sic-ing.

Joy Christian wrote:
Gordon Watson wrote:Fred, I'm not sure what you are getting at here. I'd welcome some elaboration, especially re this: "they use the same trickery as usual to show a "violation" of Bell-CHSH." Doesn't QM theory and practice violate Bell-CHSH? Thanks.

Gordon,

Nothing can violate a mathematical inequality. It is insane even to suggest that something can "violate" a mathematical inequality.

So, no. Neither quantum mechanics nor any experiment violates Bell-CHSH inequality. How can they?

It seems that in this forum only Michel, Fred, and I understand this.

To be sure, quantum mechanics makes a different prediction (as does my local model) for the Bell-CHSH string of expectation values; namely, CHSH < 2\/2 (not 2).

But that is not the same thing as claiming that quantum mechanics "violates" CHSH < 2. It simply means that CHSH < 2 is just wrong.

I will let Fred elaborate on the trickery of how experimentalists switch to CHSH < 4 in practice. Although Michel has explained this dozens of times in this forum.

Joy


FrediFizzx wrote:
Joy Christian wrote: I will let Fred elaborate on the trickery of how experimentalists switch to CHSH < 4 in practice. Although Michel has explained this dozens of times in this forum.

Let me qualify that an inequality of Bell's type is mathematically impossible to violate. That is just the trickery; they shift to a different inequality where the bound is 4 for CHSH. In Bell-CHSH, the expectation terms are dependent on elements in each other so you have a bound of 2. For QM and the experiments, the expectation terms are independent thus by simple mathematical inspection one can have,

+1 -(-1) +1 +1 = 4


Dear Joy and Fred,

Fact 1: From their Abstract, here's what CHSH - http://users.unimi.it/aqm/wp-content/uploads/CHSH.pdf - did (with my emphasis).

    "A theorem of Bell, proving that certain predictions of QM are inconsistent with the entire family [sic] of local hidden-variable theories, is generalized so as to apply to realizable experiments. A proposed extension … polarisation correlation … will provide a decisive test between QM and local hidden-variable theories [sic]."

Fact 2: The usual form of the CHSH inequality (eg, https://en.wikipedia.org/wiki/CHSH_inequality) is:

|E(a, b) - E(a, b') + E(a', b) + E(a', b')| ≤ 2; (1)

where a and a′ are detector settings on Alice's side, b and b′ on Bob's side B.

Fact 3: It is not essential but some might like to add "the four combinations may be tested in separate sub-experiments".

Fact 4: The terms in LHS (1) are unqualified: so they apply - without restriction - to relevant theories and relevant realisable experiments.

Fact 5: Experiments (eg, by Aspect, with photons pairwise correlated in a singlet state), have breached (1).

HTH, Gordon
.
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Re: CHSH - the facts!

Postby FrediFizzx » Fri Jun 03, 2016 6:38 pm

Gordon Watson wrote:Fact 5: Experiments (eg, by Aspect, with photons pairwise correlated in a singlet state), have breached (1).

Fact: Neither QM nor any experiment has ever "breached" your eq. (1) CHSH. Please demonstrate how that could ever be possible. You will be forced to engage in the same mathematical trickery that has gone on since 1974. With each expectation term being able to range from -1 to +1, do you agree that the following is possible?

+1 - (-1) + 1 + 1 = 4
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Re: CHSH - the facts!

Postby Gordon Watson » Fri Jun 03, 2016 7:12 pm

FrediFizzx wrote:
Gordon Watson wrote:Fact 5: Experiments (eg, by Aspect, with photons pairwise correlated in a singlet state), have breached (1).

Fact: Neither QM nor any experiment has ever "breached" your eq. (1) CHSH. Please demonstrate how that could ever be possible. You will be forced to engage in the same mathematical trickery that has gone on since 1974. With each expectation term being able to range from -1 to +1, do you agree that the following is possible?

+1 - (-1) + 1 + 1 = 4.


1. Re a demonstration: Let E(a, b) = -a.b; etc.

2. Re my equation (1), you appear to be focussed on the expectations under <EPRB>_Bellian and somehow avoiding <EPRB>_ Quantum. CHSH removes any such limitation: there is no subscripted limiting qualifier attached to any term on LHS (1). Please see the quantum-based experiment that they accepted as a suitable test case!

3. You appear to be overlooking the fact that CHSH present (1) - or similar - in the context of any realisable experiment (see #2 here).

4. Are you saying that, in the context of (1), there is no realisable experiment or theory that breaches it?

5. So that I am clear on where you are coming from, are you saying that Joy's theory (disproof of Bell) does not breach (1)?

6. In the context of (1), your figure of 4 would be an interesting experimental result, so I'd be pleased to learn of the related experiment that has delivered it over the four expectations on LHS (1); with a & a' and b & b' freely chosen by space-like separated Alice and Bob (respectively) - as CHSH allows.
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Re: CHSH - the facts!

Postby FrediFizzx » Fri Jun 03, 2016 7:41 pm

Gordon, you have not demonstrated any violation of CHSH. With each expectation term being able to range from -1 to +1, do you agree that the following is possible?

+1 - (-1) + 1 + 1 = 4

Please answer that question with a yes or no.

Joy's model does not violate CHSH since it is mathematically impossible for anything to violate it. It simply shows that a classical local realistic model can produce the same prediction as QM. That is how Bell's theory is disproved and how we know the inequalities can't be violated.
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Re: CHSH - the facts!

Postby Joy Christian » Fri Jun 03, 2016 9:23 pm

FrediFizzx wrote:Gordon, you have not demonstrated any violation of CHSH. With each expectation term being able to range from -1 to +1, do you agree that the following is possible?

+1 - (-1) + 1 + 1 = 4

Please answer that question with a yes or no.

Joy's model does not violate CHSH since it is mathematically impossible for anything to violate it. It simply shows that a classical local realistic model can produce the same prediction as QM. That is how Bell's theory is disproved and how we know the inequalities can't be violated.

Gordon, Just to reassure you, I agree with Fred.

1) Nothing can violate CHSH < 2. Nothing here means nothing, and includes QM, my local model, and experiments. Nothing can violate a mathematical inequality.

2) CHSH < 2 has nothing whatsoever to do with physics. The word "nothing" here includes both "classical" and "quantum" physics.

3) The correct inequality is CHSH < 4. Again, nothing can violate this inequality, and nobody has ever claimed anything has, or can violate it.

For my view of the real boo-boo Bell made (and his followers continue to make), please carefully read my latest explanation: viewtopic.php?f=6&t=267#p6435.

PS: Actually, I am being too geneorus to Bell and his followers. Either knowingly or unknowingly, what they do in their "proofs" is a truly disgraceful slight-of-hand.

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Re: CHSH - the facts!

Postby Boolean » Mon Jul 18, 2016 5:33 am

Joy Christian wrote:1) Nothing can violate CHSH < 2. Nothing here means nothing, and includes QM, my local model, and experiments. Nothing can violate a mathematical inequality.

Well, that's not really right. What is correct is that as long as the assumptions that went into the derivation of the inequality hold, nothing can violate it -- but switching to a different framework, the inequality may no longer be applicable. As an example, say you have a theory about ball bearings, namely, that no container ever can hold more than four of them. So, you can derive the following inequality: x + y < 9, where x and y stand for the number of bearings in some container, which must hold absolutely if your assumption is correct.

Now, I happen to have a container with five ball bearings, and one with four. I do the experiment, count the balls in total, and lo and behold: I have violated a mathematical inequality! But obviously, I just have falsified the hypothesis that went into the formulation of the inequality -- nothing more, nothing mysterious.

The hypothesis that goes into the CHSH inequality (or, in fact, every Bell inequality) is that there exists a joint probability such that all observable probability distributions can be produced from it via marginalization. That is, if you have four variables A, B, C and D, there exists some P(A,B,C,D) such that you only need to, e.g., sum over the possible values of C and D to obtain the probability distribution for A and B, i.e. P(A,B) (and the same for other pairs, or even singles, of variables). If this holds, then there exist certain inequalities that can't be violated (something that was actually realized in the 1860s by George Boole).

But this fails to hold in quantum mechanics -- it's simple to show that there is no such probability distribution that produces all of the marginals that QM predicts. The best you can do is obtain a quasi-probability distribution, like e.g. the Wigner distribution, which can yield negative values (but is still normalized to one). So, since the assumption of having a joint PD doesn't hold in QM, likewise Bell inequalities don't -- it's just the same as the above example with the ball bearings. It's just a modus tollens argument, really.
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Re: CHSH - the facts!

Postby FrediFizzx » Mon Jul 18, 2016 1:46 pm

Boolean wrote:
Joy Christian wrote:1) Nothing can violate CHSH < 2. Nothing here means nothing, and includes QM, my local model, and experiments. Nothing can violate a mathematical inequality.

Well, that's not really right. What is correct is that as long as the assumptions that went into the derivation of the inequality hold, nothing can violate it -- but switching to a different framework, the inequality may no longer be applicable.


I guess you don't even pay attention to your own words. ".. the inequality may no longer be applicable." Bingo! It is mathematically impossible for anything to violate a Bell type inequality. No matter how hard you try, you cannot prove that QM "violates" any Bell inequality. Of course you can do it if you cheat and say the assumptions that hold for deriving the inequality also apply to QM. But they don't, do they? The bottom line is that it is impossible for a quantum experiment to test the quadruple of Bell-CHSH. Thus they are not valid tests for local-realism.
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Re: CHSH - the facts!

Postby Joy Christian » Mon Jul 18, 2016 2:23 pm

Boolean wrote:... it's simple to show that there is no such probability distribution that produces all of the marginals that QM predicts. The best you can do is obtain a quasi-probability distribution, like e.g. the Wigner distribution, which can yield negative values (but is still normalized to one).

Thank you for your comments. I am however not impressed by the above claim. I invite you to read this paper of mine (which is also available as an arXiv preprint).

Please read this paper and tell me what is it that quantum mechanics predicts but my local model for the EPR-Bohm correlation does not predict (my local-realistic framework is in fact quite comprehensive, but let us stick to the EPR-Bohm scenario).

Quantum mechanics predicts 13 different probabilities for the EPR-Bohm scenario, and so does my model, as verified in this paper, both analytically and numerically.

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Re: CHSH - the facts!

Postby FrediFizzx » Mon Jul 18, 2016 4:26 pm

guest1202 your anonymous post was denied. What Jochen (Boolean) posted was just more repetition of what you have been posting. Try something new if you would like to convince us. But guess what? You are wrong so you won't be able to.

Look folks, it is very simple to see why Bell's argument is totally wrong beside the fact that Joy's classical local realistic model produces all the predictions of QM for the EPR-Bohm scenario. Now for the Quantum Fredi Challenge! :lol:

The whole simple idea (you don't have to even invoke all the probabilistic math) behind Bell's argument is that a classical local-realistic model is determinant. IOW, it can give predictions for individual outcome results even if you can't measure them. The problem there is that how do you test the predictions if you can't measure them? Remember that we are in the quantum domain for EPR-Bohm. So Bell's whole argument falls apart when he tries to compare LHV models to quantum models since it is impossible to test local-realistic predictions using quantum methods. The challenge is for someone to actually show that a quantum experiment could actually test for these local-realistic predictions that can't be measured. :lol:
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CHSH - the facts!

Postby guest1202 » Mon Jul 18, 2016 6:24 pm

Joy Christian wrote:Boolean wrote:
... it's simple to show that there is no such probability distribution that produces all of the marginals that QM predicts. The best you can do is obtain a quasi-probability distribution, like e.g. the Wigner distribution, which can yield negative values (but is still normalized to one).



Joy Christian wrote:Thank you for your comments. I am however not impressed by the above claim. I invite you to read this paper of mine (which is also available as an arXiv preprint) ...

Please read this paper and tell me what is it that quantum mechanics predicts but my local model for the EPR-Bohm correlation does not predict


User "Boolean" has concisely and correctly stated the reason that quantum mecanics is not (local) "realistic" in the sense that the term "local-realistic" is universally used outside of this forum. I shall use his condensed notation. He has pointed out that quantum mechanics predicts certain pseudo-marginal distributions, which he denotes P(A,B), etc. The definition of a "realistic" theory is is that these pseudo-marginals are true marginal distributions for some probability function P(A,B,C,D). That is, summing p(A,B,C,D) over all C and D produces P(A,B), etc.

The main issue with Dr. Christian's claim to have produced the results of quantum mechanics via a "local-realistic"
theory is not whether his theory reproduces quantum mechanics, but whether it is "local-realistic". His papers do not address the issue of producing P(A,B,C,D). Bell's theorem states that there is no P(A,B,C,D) which reproduces the quantum pseudo-marginals.

[...]
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Re: CHSH - the facts!

Postby Joy Christian » Mon Jul 18, 2016 6:35 pm

FrediFizzx wrote:guest1202 your anonymous post was denied. What Jochen (Boolean) posted was just more repetition of what you have been posting.

guest1202 and Jochen (Boolean) are in serious denial. Fred's challenge above is open to all. Meet the challenge first if you wish to have a further dialogue with us.

Meanwhile, these are the facts:

(1) Bell's so-called theorem has been repeatedly shown in this forum to be nothing but a conjuring trick. See for example, viewtopic.php?f=6&t=267&p=6566#p6566

(2) In two published papers and a monograph I have put forward a comprehensive local-realistic framework that reproduces ALL conceivable quantum correlations:

http://lccn.loc.gov/2012001131

http://dx.doi.org/10.1016/j.aop.2016.06.021

http://link.springer.com/article/10.100 ... 014-2412-2

I have repeatedly demonstrated in this forum that my local-realistic framework is both local and realistic in the senses explicated by Einstein and Bell.

I think it is high time to stop empty waffles like those of guest1202 and Jochen (Boolean) and accept the above facts.

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Re: CHSH - the facts!

Postby Boolean » Tue Jul 19, 2016 2:34 am

Or let's make this more simple. In the CHSH-setting, there are 16 possible cases:

Code: Select all
  A1 A2 B1 B2  | P(A1,A2,B1,B2)
   +  +  +  +  |      p1
   +  +  +  -  |      p2
   +  +  -  +  |      p3
   +  +  -  -  |      p4
   +  -  +  +  |      p5
   +  -  +  -  |      p6
   +  -  -  +  |      p7
   +  -  -  -  |      p8
   -  +  +  +  |      p9
   -  +  +  -  |      p10
   -  +  -  +  |      p11
   -  +  -  -  |      p12
   -  -  +  +  |      p13
   -  -  +  -  |      p14
   -  -  -  +  |      p15
   -  -  -  -  |      p16


Any purported local realistic model must assign fixed values between (and including) 0 and 1 to all of the pi, such that their sum equals unity. Thus, to convince me that there is a local realistic model that violates the CHSH inequality, you only need to compute those 16 probabilities, and show that the value they assign to the CHSH-correlator exceeds two in magnitude.

Of course, this is impossible: simple algebra shows that you can write the CHSH prediction as (as shown in the paper I referenced earlier)

CHSH = 2 - 4*(p4 + p5 + p6 + p8 + p9 + p11 + p12 + p13),

or equivalently as

CHSH = 4*(p1 + p2 + p3 + p7 + p10 + p14 + p15 + p16) - 2.

Clearly, if the sum of the probabilities in either case is between 0 and 1, then the expression is bounded by 2 in magnitude. Thus, you need to either violate the normalization, or admit negative values, in order to exceed that bound.
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Re: CHSH - the facts!

Postby FrediFizzx » Tue Jul 19, 2016 3:17 pm

Boolean wrote:Or let's make this more simple. In the CHSH-setting, there are 16 possible cases:

Code: Select all
  A1 A2 B1 B2  | P(A1,A2,B1,B2)
   +  +  +  +  |      p1
   +  +  +  -  |      p2
   +  +  -  +  |      p3
   +  +  -  -  |      p4
   +  -  +  +  |      p5
   +  -  +  -  |      p6
   +  -  -  +  |      p7
   +  -  -  -  |      p8
   -  +  +  +  |      p9
   -  +  +  -  |      p10
   -  +  -  +  |      p11
   -  +  -  -  |      p12
   -  -  +  +  |      p13
   -  -  +  -  |      p14
   -  -  -  +  |      p15
   -  -  -  -  |      p16


Any purported local realistic model must assign fixed values between (and including) 0 and 1 to all of the pi, such that their sum equals unity. Thus, to convince me that there is a local realistic model that violates the CHSH inequality, you only need to compute those 16 probabilities, and show that the value they assign to the CHSH-correlator exceeds two in magnitude.

Of course, this is impossible: simple algebra shows that you can write the CHSH prediction as (as shown in the paper I referenced earlier)

CHSH = 2 - 4*(p4 + p5 + p6 + p8 + p9 + p11 + p12 + p13),

or equivalently as

CHSH = 4*(p1 + p2 + p3 + p7 + p10 + p14 + p15 + p16) - 2.

Clearly, if the sum of the probabilities in either case is between 0 and 1, then the expression is bounded by 2 in magnitude. Thus, you need to either violate the normalization, or admit negative values, in order to exceed that bound.

Wonderful! You have successfully proven that nothing can violate the Bell-CHSH bound of 2. But there is no disputing that fact. This even lends to the Quantum Fredi Challenge. Please demonstrate how a quantum experiment could test P(A1,A2,B1,B2) for p1, p2...p16. Let alone "violate" it. It can't be done without cheating.
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Re: CHSH - the facts!

Postby FrediFizzx » Tue Jul 19, 2016 3:46 pm

guest1202 your post was again disapproved. Your only chance to see where you are going wrong or to prove that we are wrong is to answer the Quantum Fredi Challenge.
Please demonstrate how a quantum experiment could test P(A1,A2,B1,B2) for p1, p2...p16 referencing to Boolean's post above. And show how a quantum experiment could thus "violate" Bell-CHSH.

Also please stay on topic for this thread.
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Re: CHSH - the facts!

Postby Joy Christian » Tue Jul 19, 2016 5:22 pm

Boolean wrote:Thus, to convince me that there is a local realistic model that violates the CHSH inequality, you only need to compute those 16 probabilities, and show that the value they assign to the CHSH-correlator exceeds two in magnitude.

As I suspected, "Boolean" has not even bothered to read what I have written in my previous posts. It is very difficult to have any rational argument with such a person.

The bottom line is that the mathematical bound on the CHSH-correlator is 4, not 2:

- 4 < E(a, b) + E(a, b') + E(a', b) - E(a', b' ) < + 4 .

On the other hand, the physical bound on the CHSH-correlator is 2\/2, not 2 or 4:

- 2\/2 < E(a, b) + E(a, b') + E(a', b) - E(a', b' ) < + 2\/2 .

The bound of 2 has nothing to do with anything. It cannot be derived without employing a Uri Geller type conjuring trick. It has nothing whatsoever to do with physics:

- 2 < E(a, b, a', b' ) < + 2 .

Note that E(a, b, a', b' ) is not the same as E(a, b) + E(a, b') + E(a', b) - E(a', b' ). Only an extraordinarily stupid person would confuse the former with the latter.

There is absolutely no way to derive the upper bound of 2 on CHSH-correlator without cheating.

The reader is strongly advised to carefully read these two-pages and recognize that Bell and his followers have been cheating you for the past fifty years.

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Re: CHSH - the facts!

Postby FrediFizzx » Tue Jul 19, 2016 10:18 pm

Boolean your post was disapproved. It is complete nonsense. If you think it is not, then beat the Quantum Fredi Challenge. LOL! If you want to keep presenting a "rigged" game, then we can present a "rigged" game back at you.

For the last time; NOTHING CAN VIOLATE ANY BELL INEQUALITY! You have proven that it is mathematically impossible yourself. If you think quantum mechanics can, then I got some great bridges to sell you. :lol:
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Re: CHSH - the facts!

Postby minkwe » Fri Jul 22, 2016 10:10 am

Boolean wrote:Or let's make this more simple. In the CHSH-setting, there are 16 possible cases:

Code: Select all
  A1 A2 B1 B2  | P(A1,A2,B1,B2)
   +  +  +  +  |      p1
   +  +  +  -  |      p2
   +  +  -  +  |      p3
   +  +  -  -  |      p4
   +  -  +  +  |      p5
   +  -  +  -  |      p6
   +  -  -  +  |      p7
   +  -  -  -  |      p8
   -  +  +  +  |      p9
   -  +  +  -  |      p10
   -  +  -  +  |      p11
   -  +  -  -  |      p12
   -  -  +  +  |      p13
   -  -  +  -  |      p14
   -  -  -  +  |      p15
   -  -  -  -  |      p16


Any purported local realistic model must assign fixed values between (and including) 0 and 1 to all of the pi, such that their sum equals unity. Thus, to convince me that there is a local realistic model that violates the CHSH inequality, you only need to compute those 16 probabilities, and show that the value they assign to the CHSH-correlator exceeds two in magnitude.

Of course, this is impossible: simple algebra shows that you can write the CHSH prediction as (as shown in the paper I referenced earlier)

CHSH = 2 - 4*(p4 + p5 + p6 + p8 + p9 + p11 + p12 + p13),

or equivalently as

CHSH = 4*(p1 + p2 + p3 + p7 + p10 + p14 + p15 + p16) - 2.

Clearly, if the sum of the probabilities in either case is between 0 and 1, then the expression is bounded by 2 in magnitude. Thus, you need to either violate the normalization, or admit negative values, in order to exceed that bound.


LOL, please describe the experiment that is supposed to produce those outcomes, and also present the table of QM predicted outcomes for the same experiment. Some people never learn. I doubt you understand what "probability" means.
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Re: CHSH - the facts!

Postby FrediFizzx » Fri Jul 22, 2016 10:29 am

minkwe wrote:LOL, please describe the experiment that is supposed to produce those outcomes, and also present the table of QM predicted outcomes for the same experiment. Some people never learn. I doubt you understand what "probability" means.

Yeah, these guys claim it is some kind of definition of local-realistic and keep thinking that Joy's model should have to conform to it. NOT! It is the result of assuming that Nature is non-local and non-realistic. If one makes the simple and perfectly reasonable assumption that Nature is local and realistic then the quantum experiments prove that Bell's description of what is local and realistic is flawed. Einstein was right after all!

To lurkers out there; please don't make the assumption that Nature is non-local and non-realistic and you will be fine.
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Re: CHSH - the facts!

Postby Joy Christian » Fri Jul 22, 2016 11:09 am

FrediFizzx wrote:
minkwe wrote:LOL, please describe the experiment that is supposed to produce those outcomes, and also present the table of QM predicted outcomes for the same experiment. Some people never learn. I doubt you understand what "probability" means.

Yeah, these guys claim it is some kind of definition of local-realistic and keep thinking that Joy's model should have to conform to it. NOT! It is the result of assuming that Nature is non-local and non-realistic. If one makes the simple and perfectly reasonable assumption that Nature is local and realistic then the quantum experiments prove that Bell's description of what is local and realistic is flawed. Einstein was right after all!

To lurkers out there; please don't make the assumption that Nature is non-local and non-realistic and you will be fine.

The grotesque slight-of-hand employed by Bell and his followers is quite easy to see, provided one is not brainwashed and dazzled by the allure of Bell-type mysticism.

The four EPR-Bohm type experiments that are physically meaningful can be described by the averages

E(a, b) = << A(a)B(b) >> ,

E(a, b' ) = << A(a)B(b' ) >> ,

E(a', b) = << A(a' )B(b) >> ,

and

E(a', b' ) = << A(a' )B(b' ) >> ,

where A and B are equal to +1 or -1.

The corresponding CHSH-correlator is then bounded by 4 (or 2\/2 if you do not neglect the crucial geometrical and topological properties of the physical space):

- 4 < E(a, b) + E(a, b' ) + E(a', b) - E(a', b' ) < + 4 .

But Bell-believers derive their inequalities (or the bound of 2) by discarding the above four possible experiments altogether and replacing them with a completely different, physically entirely meaningless experiment described by the single average

E( a, b, a', b' ) = << A(a)B(b) + A(a)B(b' ) + A(a' )B(b) - A(a' )B(b' ) >>.

Note that this single average has nothing whatsoever to do with the EPR-Bohm experiment. In fact, it does not pertain to any physically possible experiment at all.

How dumb does one have to be to fall for such a blatant con?

***
Joy Christian
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Re: CHSH - the facts!

Postby Heinera » Fri Jul 22, 2016 11:37 am

minkwe wrote:LOL, please describe the experiment that is supposed to produce those outcomes, and also present the table of QM predicted outcomes for the same experiment. Some people never learn. I doubt you understand what "probability" means.

Joy Christians exploding balls experiment is supposed to produce those outcomes. You can find a more detailed description in his papers on arXiv.
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